 TOPICS # Minimax Theorem

The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928.

Formally, let and be mixed strategies for players A and B. Let be the payoff matrix. Then where is called the value of the game and and are called the solutions. It also turns out that if there is more than one optimal mixed strategy, there are infinitely many.

In the Season 4 opening episode "Trust Metric" (2007) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that he used the minimax theorem in an attempt to derive an equation describing friendship.

Game, Game Theory, Mixed Strategy

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## References

Willem, M. Minimax Theorem. Boston, MA: Birkhäuser, 1996.

Minimax Theorem

## Cite this as:

Weisstein, Eric W. "Minimax Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MinimaxTheorem.html